We have here explored one of the testable signatures of our secluded WIMP models in quantitative detail. We have considered the \(\gamma \) -rays that would be produced as a result of cosmic annihilations of secluded WIMPs of mass of \(\sim \)  20 and \(\sim \)  32 GeV. In particular, we have shown that the secluded DM model proposed here can potentially explain both the flux and spectrum of an apparent 2 – 3 GeV energy \(\gamma \) -ray excess in the galactic center region, this being an excess over that expected by taking account of other galactic \(\gamma \) -ray production processes. Such an excess has been inferred from an analysis of Fermi-LAT Gamma-ray Space Telescope data [1]}. Our results are also consistent with a putative weak \(\sim \) (2–3)\(~\sigma \)  \(\gamma \) -ray signal claimed for the dwarf galaxy Reticulum 2 [2]} and with the conservative constraints derived from Fermi Gamma-Ray Space Telescope observations in Refs. [3]}.
